Simplify the following expression: $z = \dfrac{-27t - 30}{3t + 3}$ You can assume $t \neq 0$.
Explanation: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-27t - 30 = - (3\cdot3\cdot3 \cdot t) - (2\cdot3\cdot5)$ The denominator can be factored: $3t + 3 = (3 \cdot t) + (3)$ The greatest common factor of all the terms is $3$ Factoring out $3$ gives us: $z = \dfrac{(3)(-9t - 10)}{(3)(t + 1)}$ Dividing both the numerator and denominator by $3$ gives: $z = \dfrac{-9t - 10}{t + 1}$